We note that, compared with the double Wronskian solutions of the AKNS hierarchy
(cf. Eq.(20) in [1]}),
the solutions presented in (REF ) for the pKN\((-1)\)  system are more complicated.
To implement a reasonable reduction, let us take \(M=N\)  and assume
\(A^2=\delta SS^*,~~ \delta =\pm 1,\) 
